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Temididiscussione Del Servizio Studi Temididiscussione del Servizio Studi Introduction to social choice and welfare by Kotaro Suzumura Number 442 - March 2002 The purpose of the Temi di discussione series is to promote the circulation of working papers prepared within the Bank of Italy or presented in Bank seminars by outside economists with the aim of stimulating comments and suggestions. The views expressed in the articles are those of the authors and do not involve the responsibility of the Bank. Editorial Board: ANDREA BRANDOLINI,FABRIZIO BALASSONE,MATTEO BUGAMELLI,FABIO BUSETTI,RICCARDO CRISTADORO,LUCA DEDOLA,FABIO FORNARI,PATRIZIO PAGANO;RAFFAELA BISCEGLIA (Editorial Assistant). 2 INTRODUCTION TO SOCIAL CHOICE AND WELFARE by Kotaro Suzumura ∗ Abstract Social choice theory is concerned with the evaluation of alternative methods of collective decision-making, as well as with the logical foundations of welfare economics. In turn, welfare economics is concerned with the critical scrutiny of the performance of actual and/or imaginary economic systems, as well as with the critique, design and implementation of alternative economic policies. The Handbook of Social Choice and Welfare, which is edited by Kenneth Arrow, Amartya Sen and Kotaro Suzumura, presents, in two volumes, essays on past and on-going work in social choice theory and welfare economics. This paper is written as an extensive introduction to the Handbook with the purpose of placing the broad issues examined in the two volumes in better perspective, discussing the historical background of social choice theory, the vistas opened by Arrow’s Social Choice and Individual Values, the famous “socialist planning” controversy, and the theoretical and practical significance of social choice theory. JEL classification: B21, D31, D6, D7, D81, H41, I3. Keywords: social choice theory, welfare economics, socialist planning controversy, social welfare function, Arrovian impossibility theorems, voting schemes, implementation theory, equity and justice, welfare and rights, functioning and capability, procedural fairness. Contents 1. Historical Background ............................................................................................................7 2. Social Choice and Individual Values....................................................................................13 3. “Socialist Planning” Controversy.........................................................................................17 4. Significance of the Subject and Main Lines of Research .....................................................22 5. A Disclaimer.........................................................................................................................28 References.................................................................................................................................36 ∗ Institute of Economic Research Hitotsubashi University, Tokyo, Japan. 1. Historical Background Social choice theory is concerned with the evaluation of alternative methods of collec- tive decision-making, as well as with the logical foundations of welfare economics. In turn, welfare economics is concerned with the critical scrutiny of the performance of actual and/or imaginary economic systems, as well as with the critique, design and implementation of alter- native economic policies. This being the case, it goes without saying that the origin of social choice theory can be traced back all the way to antiquity. Indeed, as soon as multiple individ- uals are involved in making decisions for their common cause, one or other method of collec- tive decision-making cannot but be invoked. As a reflection of this obvious fact, there are numerous examples in classic writings on the use and usefulness of alternative methods of collective decision-making. Suffice it to quote Aristotle in ancient Greece, and Kautilya in an- cient India; they both lived in the fourth century B.C. and explored several possibilities of collective decision-making in their books entitled, respectively, Politics and Economics.1 Likewise, as soon as any collective body designs and implements an economic mechanism and/or an economic policy, paying proper attention to the costs and benefits accruing to its constituent members, one or more social welfare judgements cannot be avoided. In this sense, Joseph Schumpeter (1954, p.1069) was certainly right when he emphasized “the hallowed antiquity of welfare economics.” He observed that “a large part of the work of Carafa and his successors as well as of the work of the scholastic doctors and their successors was welfare economics. We also know that the welfare point of view was much in evidence in the eighteenth century .... For Bentham and the English utilitarians generally this point of view was, of course, an essential element of their creed. Hence, the positive spirit of Ricardian economics notwithstanding, we find it also in the English ‘classics,’ particularly in J. S. Mill. So far as this goes, modern welfare economists merely revive the Benthamite tradition.” It was in similar vein that Paul Samuelson (1947, p.203) began his famous Chapter VIII on Welfare Economics in Foundations of Economic Analysis with the following remark: “Beginning as it did in the writings of philosophers, teleologians, pamphleteers, special pleaders, and re- formers, economics has always been concerned with problems of public policy and welfare.” Without contradicting these authoritative verdicts on the long historical background of social choice theory, we may nevertheless claim that the instrumental concern with concrete methods of collective decision-making is one thing, and theoretical investigation into their logi- cal performance is another thing altogether. The former concern may be as old as the origin of human society, but the latter development seems to be of more recent origin. Indeed, it seems fair to say that the real origin of the collective decision-making side of the coin can be attributed to the pioneering contributions by two eminent French precursors around the time of French revolution, viz. Marie-Jean de Condorcet, and Jean-Charles de Borda.2 It was in the intellec- 7 tual atmosphere of the European Enlightenment during the eighteenth century, with its con- spicuous concern with human rights and its reasoned design and implementation of rational social order, that Condorcet (1785) addressed the mathematical discipline of collective decision- making in terms of simple majority voting and related procedures.3 He discovered the paradox of voting, or the Condorcet paradox, to the effect that the method of pairwise simple majority voting may yield a social preference cycle --- a social alternative A defeating another alternative B by a simple majority, B defeating the third alternative C again by a simple majority, and C in its turn defeating A by a simple majority. This paradox sent an unambiguous signal that the logical performance of voting and related procedures for collective decision-making must be the subject of theoretical scrutiny. One of the logical implications of the Condorcet paradox is that, once a simple majority cycle occurs in the set of social alternatives S = {A, B, C}, there exists no Condorcet winner --- a feasible alternative which is undefeated by any other feasible alterna- tive --- thereby excluding the possibility of basing social choice on the seemingly democratic method of collective decision-making. It is worthwhile to recollect in passing that Condorcet’s first extended illustration of the paradox of voting was taken from voting on economic policy. Indeed, the three policy alternatives were:4 A = any restriction placed on commerce is an injustice; B = only those restrictions placed through general laws can be just; C = restrictions placed by particular orders can be just. Condorcet’s contribution seems to have been, at least partly and indirectly, inspired by an earlier work by Borda (1781), who proposed what came to be known as the Borda method of rank-order decision-making.5 For each voter, this method assigns a score of zero to the last ranked alternative, a score of one to the penultimate alternative, and so on all the way up to the top ranked alternative, which receives a score of n - 1 when there are n alternatives altogether. These individual scores are added for each candidate over all voters, and the candidate which earned the largest sum-total becomes the overall winner in the contest. According to Duncan Black (1958, p.180), “[s]oon after hearing Borda’s paper in 1794 the [French] Academy [of Sciences] adopted his method in elections to its membership. It remained in use until 1800, when it was attacked by a new member and was modified soon afterwards. The new member was Napoleon Bonaparte.” The same rank-order voting procedure was obtained from slightly different premises by Pierre-Simon Laplace (1812).6 Laplace also acutely observed an obstacle to the use of this pro- cedure to the effect that “its working might be frustrated by electors placing the strongest opponents to their favourite candidates at the foot of their list. This would give a great advan- 8 tage to candidates of mediocre merit, for while getting few top places they would also get few lowest places [Black (1958, p.182)].” As a matter of fact, the same difficulty was confronted by Borda himself, who, when his procedure was opposed precisely for this reason of strategic vulnerability, had retorted by saying that his scheme is “only intended for honest men [Black (1958, p.182)].” This episode seems to
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